Find the zeros of each of the following quadratic polynomial and verify the relationship between the zeros and their coefficients:

$q\left(y\right)=7y^2-\frac{11}{3}y-\frac{2}{3}$

Find a quadratic polynomial whose sum and product of zeroes are $\frac{-8}{3} \text{and} \frac{4}{3}$ respectively. Also, find the zeroes of the polynomial by factorisation.

For the following, find a quadratic polynomial whose sum and product of the zeroes are $\frac{21}{8}, \frac{5}{16}$ respectively. Also, find the zeroes of these polynomials by factorisation.

Find a quadratic polynomial whose sum and product of the zeroes are$-2\sqrt{3} \text{and} -9$ respectively. Also, find the zeroes of these polynomials by factorisation.

Find a quadratic polynomial whose sum and product of the zeroes are $\frac{-3}{2\sqrt{5}},-\frac{1}{2}$ respectively. Also, find the zeroes of the polynomial by factorisation.

$\alpha$ and $\beta$ are the zeros of the quadratic polynomial $f\left(x\right)=x^2-x-4$. If the value of $\frac{1}{\alpha }+\frac{1}{\beta }-\alpha \beta =k$, then find the value of $4k$.

If $\alpha$ and $\beta$ are the zeros of the quadratic polynomial $f\left(x\right)=x^2+x-2$, find the positive value of $\frac{1}{\alpha }-\frac{1}{\beta }$.